, Volume 12, Issue 1, pp 367-384

Objects that cannot be taken apart with two hands

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Abstract

It has been conjectured that every configurationC of convex objects in 3-space with disjoint interiors can be taken apart by translation with two hands: that is, some proper subset ofC can be translated to infinity without disturbing its complement. We show that the conjecture holds for five or fewer objects and give a counterexample with six objects. We extend the counterexample to a configuration that cannot be taken apart with two hands using arbitrary isometries (rigid motions).

The research of J. Snoeyink was supported in part by an NSERC Research Grant. J. Stolfi was previously at DEC Systems Research Center, Palo Alto, CA, USA.